How to pick sample values according to the 3Sigma principle in MATLAB

The parameters of the kinetic equations of complex reaction systems are actually a problem of fitting the coefficients of the system of anomalous differential equations. This can be done by following these steps:

1. Define a custom function about the system of differential equations according to the kinetic equations.

2. Construct the objective function of its data error to be the smallest, that is.

min f(ki)= [s(ti)-si] 3, and then the coefficient ki is obtained by the least squares method

4. The ODE45 function finds x1, x2, x3,。。 The fitting value 5, calculate whether the correlation coefficient r between the experimental value and the fitting value is close to 1 is calculated by programming, and the following results are obtained:

k1=;k2=;k3=;k4=;k5=;k6=;k7=; k8=;k9=;k10=;k11=;k12=;k13=; k14=;k_1=;

1. In the relevant window, directly enter the relevant data.

2. At this time, you need to click on the double sample in the basic statistics through statistics.

3. If there is no problem in the next step, determine the corresponding parameters according to the actual situation.

4. In this way, the results of the graph will be generated, and the sample mean and variance can be calculated with MATLAB.

To calculate the mean, use the mean function, for example:

x=[1,2,3]

mean(x)=2

To calculate the variance, use the var function, for example:

x=[1,2,3,4]

var(x)=

If you need the mean and variance in special cases, such as matrices, you can call the help function to check the usage.

For example, if the matrix a is 10 rows and 10 columns, the third row of extracting a is a(3,:) the third column of extracting a is a(:,3).

a=[1 2 3;4 5 6;7 8 9]a =1 2 3

a(1:2,3)

ans =36

a(1:1,2)

ans =2

Calculating the probabilities, the range of 3 sigma includes almost more than 99% of the information in the sample.

There is no way to integrate a standard normal CDF, but it can be calculated using a numerical algorithm (i.e., analog integration). Monte Carlo can also be used to simulate sample generation.

How does MATLAB estimate the mean and variance of a sample?

The sample mean can be commanded with the mean() function.

Sample variance can be commanded with the var() function. For example: >>a = [4 -7 3; 1 4 -2; 10 7 9];

mean(a)

var(a)

Run the results.